Math Is Fun Forum

mathattack

Member

Registered: 2016-03-07

Posts: 17

Geometry, Polygon, Unit Circle, Roots of Unity proof

Hello!

I'm having some trouble with the following question, could anyone help please?

1.  A regular polygon P is inscribed in a circle ΓΓ. Let A, B, and C, be three consecutive vertices on the polygon P, and let M be a point on the arc AC of ΓΓ that does not contain B. Prove that

MA⋅MC=MB2−AB2

- I tried using law of cosines and substituting, but I got stuck here:

(MB)^2 - (AB)^2 = (MA)^2 + 2(AB)(MA)Cos(<BCM) = (MC)^2 - 2(BC)(MC)Cos(<BCM)

Any help would be great, thanks!

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Geometry, Polygon, Unit Circle, Roots of Unity proof

Last edited by thickhead (2016-07-14 01:11:41)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

mathattack

Member

Registered: 2016-03-07

Posts: 17

Re: Geometry, Polygon, Unit Circle, Roots of Unity proof

Thanks thickhead!